Optimal machine capacity expansions with nested limitations under stochastic demand

This paper studies capacity expansions for a production facility that faces uncertain customer demand for a single product family. The capacity of the facility is modeled in three tiers, as follows. The first tier consists of a set of upper bounds on production that correspond to different resource types (e.g., machine types, categories of manpower, etc.). These upper bounds are augmented in increments of fixed size (e.g., by purchasing machines of standard types). There is a second‐tier resource that constrains the first‐tier bounds (e.g., clean room floor space). The third‐tier resource bounds the availability of the second‐tier resource (e.g., the total floor space enclosed by the building, land, etc.). The second and third‐tier resources are expanded at various times in various amounts. The cost of capacity expansion at each tier has both fixed and proportional elements. The lost sales cost is used as a measure for the level of customer service. The paper presents a polynomial time algorithm (FIFEX) to minimize the total cost by computing optimal expansion times and amounts for all three types of capacity jointly. It accommodates positive lead times for each type. Demand is assumed to be nondecreasing in a “weak” sense. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

A continuous‐time strategic capacity planning model

Capacity planning decisions affect a significant portion of future revenue. In the semiconductor industry, they need to be made in the presence of both highly volatile demand and long capacity installation lead‐times. In contrast to traditional discrete‐time models, we present a continuous‐time stochastic programming model for multiple resource types and product families. We show how this approach can solve capacity planning problems of reasonable size and complexity with provable efficiency. This is achieved by an application of the divide‐and‐conquer algorithm, convexity, submodularity, and the open‐pit mining problem. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Landmarks in defense literature

The Strategy of Conflict. By Thomas Schelling. Harvard University Press, Cambridge, MA (1960)     

Conflict,technology, and the impact of industrialization: The Great War 1914–18

In major respects, World War I appeared markedly unlike even quite recent wars. What, by and large, caused the difference was not quality of command or changing morale. It was industrial mobilisation and technological advancement. The emergence of new weapons, and of new methods of producing them in volume and at speed, played a crucial role in changing the nature of war.

Certainly, the peculiar qualities of the Great War of 1914–18 were not determined solely by technology. Quite other factors, such as the profundity of the issues at stake ('This war is life and death'), and the relative equality in resources and determination between the principal rivals, also profoundly influenced the nature of the conflict. Yet in delineating the dominant aspects of that struggle, the contribution made by industrialization and technology and a culture of inventiveness must loom large.

Admittedly, in some respects, the transformation of weaponry under the impact of industrialisation did not necessarily produce a new kind of war. The battleship of 1914 was hugely unlike the battleship of 1805, yet the Great War at sea was not strikingly different from the naval war against Napoleon. War in the air was an entirely new phenomenon, yet the aircraft had not reached a state of development where it could fundamentally alter the face of battle.

But in the case of the land war, new weapons and new volumes of weaponry did indeed make a vast difference to the nature and consequence of military operations. In large measure they generated the features by which this struggle is best remembered: stalemate, immobility, great battles of attrition, and ‘futility’.     

A general strategic capacity planning model under demand uncertainty

Capacity planning decisions affect a significant portion of future revenue. In equipment intensive industries, these decisions usually need to be made in the presence of both highly volatile demand and long capacity installation lead times. For a multiple product case, we present a continuous‐time capacity planning model that addresses problems of realistic size and complexity found in current practice. Each product requires specific operations that can be performed by one or more tool groups. We consider a number of capacity allocation policies. We allow tool retirements in addition to purchases because the stochastic demand forecast for each product can be decreasing. We present a cluster‐based heuristic algorithm that can incorporate both variance reduction techniques from the simulation literature and the principles of a generalized maximum flow algorithm from the network optimization literature. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

War reserve spares kits supplemented by normal operating assets

In peacetime, base stock levels of spares are determined on the assumption of normal resupply from the depot. In the event of war, however, a unit must be prepared to operate from stock on hand for a period of time without being resupplied from the depot. This paper describes a mathematical model for determining such war reserve spares (WRS) requirements. Specifically, the model solves the following kind of optimization problem: find the least-cost WRS kits that will keep the probability of a stockout after K cannibalizations less than or equal to some target objective α. The user of the model specifies the number of allowable cannibalizations, and the level of protection that the kit is supposed to provide. One interesting feature of this model is that in the probability computation it takes into account the possiblility of utilizing normal base operating assets. Results of a sensitivity analysis indicate that if peacetime levels were explicitly taken into account when designing a WRS kit, a cost saving of nearly 40 percent could be effected without degrading base supply performance in wartime.